Problem: The grades on a physics midterm at Gardner Bullis are normally distributed with $\mu = 84$ and $\sigma = 4.5$. Emily earned a $94$ on the exam. Find the z-score for Emily's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Emily's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{94 - {84}}{{4.5}}} $ ${ z \approx 2.22}$ The z-score is $2.22$. In other words, Emily's score was $2.22$ standard deviations above the mean.